In the preceding paper, using the so-called flow variable representation, we reported the formulation of the Korteweg-deVries (KdV) and the Burgers equations to express mass transports. The transport theories were constructed by pertaining to correspondence with the Toda lattices. Our present...

We study the significant entropy changes in supercooling and glass transition by developing a two (H and L) state cluster model, where the H-state represents the clusters with the coordination number z being larger than the reference size zR and the L-state those with zzR, respectively. We...

We present a novel method of computing the asymptotic drift velocity V and the diffusion coefficient D of a particle diffusing in an arbitrary periodic medium. We focus on a particular case of 1D systems with the nearest-neighbor transition rates and explain in detail how our method works in...

An efficient methodology of estimation of parameters in the diffusion coefficient of the stochastic differential equation (SDE) is presented in this work. The methodology is based on the concept of quadratic variation of a stochastic process and on some classical numerical tools such as spline...

The problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered. For the overdamped Brownian particle moving in a piecewise linear dichotomously fluctuating metastable potential, we obtain the mean first-passage...

The mobility tensor for many spheres suspended in a viscous fluid is considered. An analytical formula for the divergence of this tensor is derived. It is then applied in calculations of long-time collective diffusion coefficient of hard-sphere suspension by means of Brownian dynamics method.

Diffusions are widely used in finance due to their tractability. Driftless diffusions are needed to describe ratios of asset prices under a martingale measure. We provide a simple example of a tractable driftless diffusion which also has a bounded state space.